If I get what you mean, I think you should do the following:

1. Offer the user a web form to fill in
2. The form should be submitted to a (CGI) script
3. The script stores the submitted data into some permanent storage, like appending it into a text file (as in Simple Feedback form.), a database, or perhaps, like diotalevi apparently suggests, mail it to a mailbox set up for this purpose.

It would be best if people were allowed to unsubscribe as well, so this simple, naive scheme probably won't be the best approach.

In that case, you'd better take a look at some existing mailing list management software. This isn't quite the place to search for prewritten scripts, so you might be better of elsewhere. In order not to discourage you too much, I'll already give you one pointer: the mailing list management software FAQ. And yes, there are quite a few of these packages that are written in Perl.